Elastic-Plastic Analysis of Steel Structures Using the Finite Element Method (4th Report) : Elastic Large Deflection of Plates

Abstract

In this series of investigation, various complicated problems have been analysed by the finite element method, such as elastic-plastic stress analysis, plate buckling under various loading and supporting conditions, etc. and new applicability of the method is being developed. In this paper, the non-linear behavior of plate is treated and special attention is paid to its elastic geometrical non-linear behavior of a plate under uniform pressure. For the analysis, the basic non-linear equation is linearized by using the concept of incremental procedure. The developed equation is of linear form with respect to its deformation and is applied at each step of loading. The accumulation of the solution for each increment of loading presents the solution of the problem. In the analysis, shape functions of the finite element should be defined with five degrees of freedom at each nodal point. In this analysis, triangular comforming shape functions for both in-plane and out-of-plane deformations are employed. The results of analysis are compared with analytical solutions obtained by other methods and this method is found to give very accurate solution when the increment of load is taken reasonably small.